Average Error: 0.0 → 0.0
Time: 14.5s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(y, \log y, x - z\right)}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(y, \log y, x - z\right)}
double f(double x, double y, double z) {
        double r12214419 = x;
        double r12214420 = y;
        double r12214421 = log(r12214420);
        double r12214422 = r12214420 * r12214421;
        double r12214423 = r12214419 + r12214422;
        double r12214424 = z;
        double r12214425 = r12214423 - r12214424;
        double r12214426 = exp(r12214425);
        return r12214426;
}
↓
double f(double x, double y, double z) {
        double r12214427 = y;
        double r12214428 = log(r12214427);
        double r12214429 = x;
        double r12214430 = z;
        double r12214431 = r12214429 - r12214430;
        double r12214432 = fma(r12214427, r12214428, r12214431);
        double r12214433 = exp(r12214432);
        return r12214433;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log y, x - z\right)}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot e^{\mathsf{fma}\left(y, \log y, x - z\right)}}\]

  5. Final simplification0.0

    \[\leadsto e^{\mathsf{fma}\left(y, \log y, x - z\right)}\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))